1. Field of the Invention
The present invention relates to a method for determining a pulse sequence for feeding a radio-frequency transmit coil having one transmit channel, or a number of transmit channels, in a magnetic resonance apparatus.
2. Description of the Prior Art
For feeding the radio-frequency transmit coils in order to produce a deflection of the spin from the equilibrium magnetization, conventional magnetic resonance (MR) apparatuses use parameters that are designed such that the produced deflection field (often also called the B1 field) is as homogenous as possible within the measurement region not occupied by a person. It is to be noted at the outset that the designation “radio-frequency transmit coil” also encompasses transmit and receive coils throughout.
Particularly in newer MR apparatuses, for example equipment having a base magnetic field strength greater than or equal to 3 tesla, it has however turned out that this homogeneity can be disrupted already by the introduction of a patient, because eddy currents are produced in the patient that in turn produce interference fields that destroy the homogeneity of the deflection field, and thus of the magnetization. This increase in the eddy current effect is due to the obligatory use of higher frequencies.
In the aforementioned, long-known cases, the feeding conventionally takes place in such a way that given n excitation channels of the coil, the successive channels are fed so as to be respectively offset by 2π/n, in order to achieve a circularly polarized field. This manner of operation produces a homogenous deflection field in empty space, and is often referred to as “mode 1.”
A first approach to solving the aforementioned problems is called the static approach. Here, the phase and amplitude are held constant for each channel for the entire duration of the excitation in order to achieve a more homogenous magnetization. However, the improvements achieved thereby are not adequate, and enable neither an optimization with respect to the SAR exposure of the patient nor as is frequently desirable, a solely local deflection of the spin.
In order to solve the last-noted problem, it has been proposed to use the gradient coils, which during the excitation are normally inactive except for the slice selection gradient, during the radio-frequency excitation pulse as well, in order to select particular regions of the slice to be excited in a time-resolved manner. In parallel, it has been proposed to permit a dynamic change in the phase and amplitude of the transmit channels during the duration of the excitation, so that a pulse sequence results. A particular region is then, so to speak, selected and correspondingly excited, and in the next time step a different region is processed. For this purpose, a k-space trajectory for the gradient coils is specified that selects the partial volumes (also called voxels) of the volume of the excited slice in a predetermined manner.
However, here the problem occurs that a highly complex equation system has to be solved. This follows directly from the known Bloch equation:
                                          ⅆ                          M              →                                            ⅆ            t                          =                  γ          ⁢                                          ⁢                      M            →                    ×                                    B              →                        1                                              (        1        )            where M is the magnetization, t is time, and {right arrow over (B)}1 designates the deflection field. Usually, the formula also contains terms that describe the relaxation, which can be neglected since the duration of the excitation is very much shorter than time constants T1 and T2. References hereinafter to the Bloch equation are to be understood as referring to equation (1). The desired homogenous, or homogenous in particular regions, magnetization accordingly results as a time integral over the duration of the pulse sequence (one millisecond, or a number of milliseconds), or, in the time-discretized (use of incremental time steps) case, as a sum over all time steps. This desired magnetization is thus prespecified, while it has to be determined which combination of B1 fields and gradient fields, from which the feed parameters for the transmit channels can then be derived, results in this magnetization.
However, due to its vector nature and the discretization in space and time that is to be carried out, the Bloch equation decomposes into a multiplicity of equations that form an equation system. If it is taken into consideration that each transmit channel (for example 8) requires a complex-valued coefficient (i.e., amplitude and phase as feed parameters) for each time unit (conventionally several 100 during a 1 ms duration of the overall excitation pulse), with the use of the Bloch equation there results an equation system having several thousand variables. The desired magnetization (e.g. homogenous), or the desired magnetization distribution (e.g. homogenous in a particular region) in the selected slice is entered into this equation system.
Pulse calculation methods known for this purpose proceed from a small-angle approximation that enables a linearization of the resulting equation system; this means that the methods begin from small deflection angles. The inputs into the equation system are then real and imaginary parts of the desired magnetization; here the magnetization is permitted to amount to only a few percent (e.g. <10%) of the equilibrium magnetization, in order to make the small angle approximation permissible.
Apart from the fact that this solution approach does not permit large deflection angles, another problem that occurs cannot be taken into account. The application of gradient fields during RF radiation results in spatially selective excitation. Therefore, the overall introduced power loss, i.e. the SAR (specific absorption rate), increases, which can result in an exceeding of prespecified boundary values and danger to the patient. In addition, phenomena known as hotspots can occur in the individually excited regions, i.e. regions in which the SAR is locally particularly high. Finally, the taking into account of further quantities that limit the excitation pulses is not possible, or is possible only with difficulty, for example in the case of limited output power of the RF amplifier.